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Original Articles

Focal decomposition, renormalization and semiclassical physics

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Pages 1019-1029 | Received 03 Feb 2009, Accepted 28 Jan 2010, Published online: 22 Feb 2011

References

  • Abraham , R. and Marsden , J. 1978 . Foundations of Mechanics , 2nd ed. , Reading, MA : Benjamin/Cummings .
  • Arnold , V.I. 1989 . Mathematical Methods of Classical Mechanics , New York : Springer Verlag .
  • Bolotin , S.V. and MacKay , R.S. 2003 . “ Isochronous potentials ” . In Localization and Energy Transfer in Nonlinear Systems , Edited by: Vazquez , L. , MacKay , R.S. and Zorzano , M.P. 217 – 224 . Singapore : World Scientific .
  • de Carvalho , C.A.A. and Cavalcanti , R.M. 1997 . Tunneling catastrophes of the partition function . Braz. J. Phys. , 27 : 373 – 378 .
  • C.A.A. de Carvalho, M.M. Peixoto, D. Pinheiro, and A.A. Pinto, An asymptotic universal focal decomposition for non-isochronous potentials, Submitted, arXiv:math/0908.0778
  • MacKay , R.S. and Meiss , J.D. 1987 . Hamiltonian Dynamical Systems: A Reprint Selection , Bristol : Adam Hilger .
  • Marsden , J. and Ratiu , T. 1999 . Introduction to Mechanics and Symmetry , New York : Springer Verlag .
  • Peixoto , M.M. 1982 . On end point boundary value problems . J. Differential Equations , 44 : 273 – 280 .
  • Peixoto , M.M. and Thom , R. Le point de vue énumératif dans les problèmes aux limites pour les équations différentielles ordinaires . C.R. Acad. Sci. Paris, Sér. I , 303 629 – 633 . Erratum, 307 (1988) 197–198; II, 303 (1986), pp. 693–698

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